MP-Review: : (Matroids Matheplanet)

This book in the German language, is a revised edition of the book by D. Rasch “Mathematische Statistik”, Joh. Ambrosius Barth (Heidelberg) , (1995), pages 851. From this book of 1995 the first seven chapters are deleted, namely “1. Mathematische Hilfsmittel, 2. Charakterisierung empirischer Verteilungen, 3. Einführung in die Wahrscheinlichkeitsvereilung, 4.Wahrscheinlichkeitsverteilungen, 5. Mehrdimensionale Verteilungen, 6. Funktionen und Folgen von zufälligen Variabelen, 7. Verteilungssysteme und Verteilungsfamilien”. The authors assumed now that the readers has already knowledge of this introductory material. The content of the revised edition contains the following chapters:

Grundbegriffe der mathematischen Statistik (38 pages)
Punktschätzung (42 pages)
Statistische Tests und Konfidenzschätzungen (94 pages)
Lineare Modelle – Allgemeine Theorie (26 pages)
Varianzanalyse – Modelle mit festen Effekten (Model I der Varianzanalyse) (84 pages)
Varianzanalyse – Schätzung von Varianzkomponenten (Model II der Varianzanalyse) (50 pages)
Varianzanalyse – Modelle mit endlichen Stufengesamtheiten und gemischte Modelle (32 pages)
Regressionsanalyse – Lineare Modelle mit nicht zufälligen Regressoren und zufälligen Regressoren (44 pages)
Regressionsanalyse – Eigentlich nichtlineares Modell I (64 pages)
Kovarianzanalyse (14 pages)
Statistische Mehrentscheidungsprobleme (50 pages)
Versuchsanalagen (42 pages)
Lösungen und Lösungsansätze zu den Übungsaufgaben (26 pages)

Anhang A Symbolik (4 pages) Anhang B Abkürzungen ( 2 pages) Anhang C Wahrscheinlichkeiten bzw. Dichtefunktionen und Verteilungen (2 pages) Anhang D Tabellen (8 pages) Sachverzeichnis (11 pages) Compared with other mathematical statistical textbooks this book not only gives the solution for the analysis of the problems when the data are gathered, but they also discussed the problem how to gather in an optimal way the data. For the Analysis of Variance models with fixed effects (Model I) the optimal designs can be derived with the R-package OPDOE (Optimal Design of Experiments). Optimal allocation has also been treated in chapters 8 and 9 about the Regression Models. Furthermore this book ended with the last chapter 13 with some Experimental Designs, especially the Balanced Incomplete Block Designs. This last chapter was not present in the first edition of the 1995 book. The interested reader can find more background of OPDOE in the book of Rasch, D., Pilz, J., et al. (2011), “ Optimal Experimental Design with R”, Chapman and Hall/CRC. The mathematical style of the book is clear. The authors gives a lucid derivation of maximum likelihood estimators, where they not stopped when the solution of the first derivative of the log-likelihood equations equal to zero has been found, but also shows that these solutions gives a maximum of the likelihood, hence that the solutions are really Maximum Likelihood Estimators. In many mathematical statistical textbooks this proof of a maximum is not given. For the Linear Models in chapter 4 they give the derivation of the Least Squares Estimators with the proof that these estimators really gives a minimum of the Sum of Squares of the deviations from the expected values estimate. In many Design of Experiments books the Least Squares Estimators are derived from the solution of the equations of the first partial derivatives of the Sum of Squares deviations equal to zero, the normal equations. But then in these books the author did not show that these solutions gives really a minimum. For the interested reader there are in each chapter exercises and solutions of these exercises This book can warmly be advised to be used as a companion for the University lectures in mathematical statistics, but also for the readers who already finished their University education and want to brush up the ideas of the mathematical background of the analysis of the mathematical statistical procedures. L. R. Verdooren emeritus Associate Professor in the Design and Analysis of Experiments of the Wageningen Agricultural University, the Netherlands.

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